In computer vision applications, estimation of geometrical characteristics of scenes and objects, such as relative pose, absolute pose and three-dimensional (3D) models, rely on underlying constraints. For example, graph-rigidity based on inter-point distances can be used for 3D reconstruction. Cheirality is one of the key concepts that enables one to identify a correct reconstruction from ambiguous ones arising from mirror reflection. In simple words, the cheirality constraint enforces that the scene is in front of the camera rather than behind it.
Divide and Concur (D&C) is a constraint satisfaction method based on difference-map (DM) dynamics. The D&C method is closely related to iterative optimization methods. In particular, the D&C method can be characterized as a message-passing method and it is similar to Belief Propagation (BP). The D&C method can be characterized as a special case of an alternating direction method of multipliers (ADMM) method. Furthermore, the D&C method is a generalization of iterative projection methods such as Douglas-Rachford for convex optimization, and Fienup's Hybrid input output (HIO) method for phase retrieval.
Generally, 3D modeling methods use the following steps. First, one estimates the poses of the cameras, and then outliers are removed. To this end, minimal approaches are critical. After obtaining some initial solution for camera poses and 3D points, bundle-adjustment can be applied.
In a 5-point solver, several challenging minimal problems are addressed using algebraic solvers. Algebraic solvers are not guaranteed to solve any polynomial system. For example, certain minimal problems such as 3-view 4-point are notoriously difficult to solve. There are other challenging problems, such as estimating the poses from six line correspondences in three views, and minimal methods for general cameras.
General cameras refer to a broad class of sensors where the projection rays do not necessarily pass through an optical center of the camera. This generality creates greater challenges when one tries to solve minimal problems. For example, the relative pose between two general cameras produces 64 solutions after solving a large polynomial system.